Measurement uncertainty evaluation based on the Monte Carlo method (MCM) with the assumption that all uncertainty sources are independent is common. For some measure problems, however, the correlation between input quantities is of great importance and even essential. The purpose of this paper is to provide an uncertainty evaluation method based on MCM that can handle correlated cases, especially for measurement in which uncertainty sources are correlated and submit to non-Gaussian distribution. In this method, a linear-nonlinear transformation technique was developed to generate correlated random variables sampling sequences with target prescribed marginal probability distribution and correlation coefficients. Measurement of the arm stretch of a precision centrifuge of 10-6 order was implemented by a high precision approach and associated uncertainty evaluation was carried out using the mentioned method and the method proposed in the Guide to the Expression of Uncertainty in Measurement (GUM). The obtained results were compared and discussed at last.